class Solution {
public:
    int minInsertions(string s)
    {
        int n = s.size();
        vector<vector<int>> dp(n, vector<int>(n, 0));
        for (int i = n - 1; i >= 0; i--)
        {
            dp[i][i] = 1;
            for (int j = i + 1; j < n; j++)
                dp[i][j] = s[i] == s[j] ? dp[i + 1][j - 1] + 2 : max(dp[i][j - 1], dp[i + 1][j]);
        }
        return s.size() - dp[0][n - 1];
    }
};